This work considers a pursuit-evasion game in which a number of pursuers are attempting to capture a single evader. Cooperation among multiple agents can be difficult to achieve, as it may require the selection of actions in the joint input space of all agents. This work presents a decentralized, real-time algorithm for cooperative pursuit of a single evader by multiple pursuers in bounded, simply-connected planar domains. The algorithm is based on minimizing the area of the generalized Voronoi partition of the evader. The pursuers share state information but compute their inputs independently. No assumptions are made about the evader's control strategies other than requiring the evader control inputs to conform to a speed limit. Proof of guaranteed capture is shown when the domain is convex and the players' motion models are kinematic. Simulation results are presented showing the efficiency and effectiveness of this strategy.

Pursuit-evasion games are an important problem in robotics and control, but games with many players are difficult to analyze and solve. This paper studies a game of multiple pursuers cooperating to capture a single evader in a bounded, convex, polytope in the plane. We present a decentralized control scheme based on the Voronoi partion of the game domain, where the pursuers jointly minimize the area of the evader's Voronoi cell. We prove that capturing the evader is guaranteed under this scheme regardless of the evader's actions, and show simulation results demonstrating the pursuit strategy.

Capture-the-flag is a complex, challenging game that is a useful proxy for many problems in robotics and other application areas. The game is adversarial, with multiple, potentially competing, objectives. This interplay between different factors makes the problem complex, even in the case of only two players. To make analysis tractable, previous approaches often make various limiting assumptions upon player actions. In this paper, we present a framework for analyzing and solving a twoplayer capture-the-flag game as a zero-sum differential game. Our problem formulation allows each player to make decisions rationally based upon the current player positions, assuming only an upper bound on the movement speeds. Using HamiltonJacobi reachability analysis, we compute winning regions for each player as subsets of the joint configuration space and derive the corresponding winning strategies. Simulation results are presented along with implications of the work as a tool for automation-aided decision-making for humans and mixed human-robot teams.

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Macrocyclic inhibitor 1 {methyl [cyclo-7[(2R)-((N-valyl) amino)-2-(hydroxyl-(1S)-1-methyoxycarbonyl-2-phenylethoxy)phosphinyloxyethyl]-1-naphthaleneacetamide] sodium salt} was designed according to the conformation of the acyclic analogue Iva-l-Val-l-Val-l-LeuP-(O)Phe-OMe [LeuP = the phosphinic acid and analogue of l-leucine; (O)Phe = l-3-phenyllactic acid; OMe = methyl ester] (4) bound to penicillopepsin, by linking the P1 and P3 side chains of the penicillopepsin inhibitor. This compound and its two acyclic derivatives, {methyl (2S)-[1-(((N-Formyl)-l-valyl)amino-2-(2-naphthyl)ethyl)hydroxyphosphinyloxy]-3-phenylpropanoate, sodium salt} (2) and {methyl (2S)-[1-(((N-(1-naphthaleneacetyl))-l-valyl)aminomethyl)hydroxyphosphinyloxy]-3-phenylpropanoate, sodium salt} (3), have been synthesized and evaluated as inhibitors of penicillopepsin. Their binding affinity to the enzyme was found to be inversely related to the predicted degree of conformational flexibility across the series:  3 (K i = 110 μM), 2 (K i = 7.6 μM), 1 (K i = 0.8 μM). The X-ray crystallographic structures of penicillopepsin complexed with the macrocyclic peptidyl phosphonate 1 and with its two derivatives 2 and 3 have been determined and refined to crystallographic agreement factors R (=Σ||F o| − |F c||/Σ|F o|) of 15.9%, 16.0%, and 15.2% and R free of 19.8%, 20.3%, and 21.4%, respectively. The intensity data for all complexes were collected to 1.5 Å resolution. One 1.25 Å resolution data set was obtained for the complex with 1 at 110 K; the structure was refined to an R factor of 15.0% (R free of 19.7%). The binding interactions that 1 and 2 make with penicillopepsin are similar to those that have been observed for other transition-state mimics with aspartyl proteinases. On the other hand, the acyclic linear inhibitor 3 exhibits distinctive binding to penicillopepsin with the phosphonate group shifted ∼3.0 Å from the average position observed for the other complexes. These structural results show that the macrocyclic constraint of 1 enhances its binding affinity over those of the acyclic analogues but the differences in the observed bound dispositions mean that the effect has yet to be quantified.